Spinc–structures and homotopy equivalences

We show that a homotopy equivalence between manifolds induces a correspondence between their spin $^{c}$ –structures, even in the presence of 2–torsion. This is proved by generalizing spin $^{c}$ –structures to Poincaré complexes. A procedure is given for explicitly computing the correspondence under reasonable hypotheses.

Keywords

4–manifold, Seiberg–Witten invariant, Poincaré complex

Mathematical Subject Classification

Primary: 57N13, 57R15

Secondary: 57P10, 57R19

References

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Publication

Received: 16 May 1997

Accepted: 17 October 1997

Published: 23 October 1997

Proposed: Ronald Stern

Seconded: Robion Kirby, Dieter Kotschick

Authors

Robert E Gompf
Department of Mathematics The University of Texas at Austin Austin Texas 78712-1082 USA

Volume 1, issue 1 (1997)

Robert E Gompf